Cloud point coexistence

On the left-hand side of Fig. 4 we have the normal phase diagram of the binary BE-H2O system. The addition of DEC shifts the two phase equilibria to higher BE concentrations and to lower temperatures. If the addition of a third component is continued beyond the cloud point, eventually three distinct phases appear. Unfortunately the cloud point technique gives us the initial concentration or temperature where unmixing begins but is not suitable to distinguish between the coexistence of two phases and three phases. Also the three phase region depends quite critically on temperature. 

D. Onset of Phase Coexistence Cloud Point and Shadow... 

In fact, the condition just described holds whenever all but one of a set of coexisting phases are of infinitesimal volume compared to the majority phase. This is because the density distribution, p (cr), of the majority phase is negligibly perturbed, whereas that in each minority phase differs from this by a Gibbs-Boltzmann factor, of exactly the form required for (10) we show this formally in Section III. Accordingly, our projection method yields exact cloud point and shadow curves. By the same argument, critical points (which in fact lie at the intersection of these two curves) are exactly determined the same is true for tricritical and higher-order critical points. Finally, spino-dals are also found exactly. We defer explicit proofs of these statements to Section III. 

One may expect intuitively that, starting from S = 0 at the cloud point, <5 should increase as one moves deeper into the coexistence region by increasing x - We find that this is so, but only as an overall trend When new phases are detected as y is increased, 5 may temporarily decrease before increasing again. This explains the crossing of the curves for X1 = 10 and x — 15 in Fig. 11. 

A plot of the temperatures required for clouding versus surfactant concentration typically exhibits a minimum in the case of nonionic surfactants (or a maximum in the case of zwitterionics) in its coexistence curve, with the temperature and surfactant concentration at which the minimum (or maximum) occurs being referred to as the critical temperature and concentration, respectively. This type of behavior is also exhibited by other nonionic surfactants, that is, nonionic polymers, // - a I k y I s u I Any lalcoh o I s, hydroxymethyl or ethyl celluloses, dimethylalkylphosphine oxides, or, most commonly, alkyl (or aryl) polyoxyethylene ethers. Likewise, certain zwitterionic surfactant solutions can also exhibit critical behavior in which an upper rather than a lower consolute boundary is present. Previously, metal ions (in the form of metal chelate complexes) were extracted and enriched from aqueous media using such a cloud point extraction approach with nonionic surfactants. Extraction efficiencies in excess of 98% for such metal ion extraction techniques were achieved with enrichment factors in the range of 45-200. In addition to metal ion enrichments, this type of micellar cloud point extraction approach has been reported to be useful for the separation of hydrophobic from hydrophilic proteins, both originally present in an aqueous solution, and also for the preconcentration of the former type of proteins. 

Winter et al. [119, 120] studied phase changes in the system PS/PVME under planar extensional as well as shear flow. They developed a lubrieated stagnation flow by the impingement of two rectangular jets in a specially built die having hyperbolic walls. Change of the turbidity of the blend was monitored at constant temperature. It has been found that flow-induced miscibility occurred after a duration of the order of seconds or minutes [119]. Miscibility was observed not only in planar extensional flow, but also near the die walls where the blend was subjected to shear flow. Moreover, the period of time required to induce miscibility was found to decrease with increasing flow rate. The LCST of PS/PVME was elevated in extensional flow as much as 12 K [120]. The shift depends on the extension rate, the strain and the blend composition. Flow-induced miscibility has been also found under shear flow between parallel plates when the samples were sheared near the equilibrium coexistence temperature. However, the effect of shear on polymer miscibility turned out to be less dramatic than the effect of extensional flow. The cloud point increased by 6 K at a shear rate of 2.9 s. ... 

Ratzsch, M. Kruger, B. Kehlen, H., "Cloud-Point Curves and Coexistence Curves of Several Polydisperse Polystyrenes in Cyclohexane," J. Macromol. Sci., Chem., A27, 683 (1990). 

Coexistence curves can accurately be determined from measurements of the refractive index in the two phases of a flame sealed critical sample. Criticality of the sample is ensured by the equal volume criteria, requiring equal volume of the phases at the cloud point. The Lorenz-Lorentz relation is employed to determine the composition in the coexisting phases. Note, measurements of cloud points for samples of different compositions usually do not suffice to reach the necessary accuracy as minute uncontrollable impurities influence the cloud point temperature. 

Figure 16.5 Comparison between the self-consistently solved coexistence line and the cloud points (filled triangle) of iPP/EPDM and the melting points (filled circles). The solidus and liquidus lines are virtually overlapped (dots), but the existence of both fines is manifested by the kink in the LCST coexistence line. The phase diagram was calculated using the material parameters, AHufp = 2110calmol , = 162.5°C, rj>p = 1800, repoM = 1000, and = 0.8 at T. ...

L Cloud-point and/or coexistence curves of quasibinary solutions... 

HAN Han, S.J., Gregg, C.J., and Radosz, M., How the solute polydispersity affects the cloud-point and coexistence pressures in propylene and ethylene solutions of alternating poly(ethylene-co-propylene),/ /. Eng. Chem. Res., 36, 5520, 1997. 

The occurrence of a secondary phase separation inside dispersed phase particles, associated with the low conversion level of the p-phase when compared to the overall conversion, explains the experimental observation that phase separation is still going on in the system even after gelation or vitrification of the a-phase [26-31]. A similar thermodynamic analysis was performed by Clarke et al. [105], who analyzed the phase behaviour of a linear monodisperse polymer with a branched polydisperse polymer, within the framework of the Flory-Huggins lattice model. The polydispersity of the branched polymer was treated with a power law statistics, cut off at some upper degree of polymerization dependent on conversion and functionality of the starting monomer. Cloud-point and coexistence curves were calculated numerically for various conversions. Spinodal curves were calculated analytically up to the gel point. It was shown that secondary phase separation was not only possible but highly probable, as previously discussed. 

Aqueous solutions of many nonionic amphiphiles at low concentration become cloudy (phase separation) upon heating at a well-defined temperature that depends on the surfactant concentration. In the temperature-concentration plane, the cloud point curve is a lower consolution curve above which the solution separates into two isotropic micellar solutions of different concentrations. The coexistence curve exhibits a minimum at a critical temperature T and a critical concentration C,. The value of Tc depends on the hydrophilic-lypophilic balance of the surfactant. A crucial point, however, is that near a cloud point transition, the properties of micellar solutions are similar to those of binary liquid mixtures in the vicinity of a critical consolution point, which are mainly governed by long-range concentration fluctuations [61]. 

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